The stimulus for this paper is the expressed need in proposals for legged vehicles both to propel the vehicle in rectilinear translation parallel to the mean ground-profile beneath it and to allow the chassis-height to be adjustable. Energy considerations point toward having a single propulsion-actuator on each leg-linkage rather than adopting the less economical option of simultaneous actuation at two or more serially connected leg-joints. Of the linkages whose kinematics are here studied some relate more closely to legged vehicles than others do; the paper should be viewed in a general rather than a specific context. Exact and approximate straight-line planar linkages are covered. Derivatives of Richard Roberts’s linkage are put forward as those that are the most promising adjustable linkages whose joints are all turning pairs.

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